Peel and cut the plantains into 4-5 thick, round slices.
Pour vegetable oil into a large saucepan until it's at least 3 inches (or about 5 cm) deep. Heat on medium until the oil is 375℉ (190℃).
Gently drop the plantain slices into the oil in batches to avoid overcrowding the pan.
Fry for a few minutes until lightly browned and cooked through (3-4 minutes on each side).
Using a large slotted spoon or something similar, remove the plantain slices from the oil to flatten them. Leave the oil on the heat because the tostones are going back in for the second fry.
Place a tostón on a cutting board or flat surface, and press down on it firmly with the back of a heavy plate, bottle, or skillet until flattened to about ¼-inch thick. Repeat with the remaining slices.
Fry the flattened pieces in the 375°F (190℃) oil, turning them occasionally, for 2-3 minutes or until golden. Then transfer them with a slotted spoon to paper towels to drain, and season them with garlic salt and pepper.